Today - Messages Additional shared lab hours in A-269 –M, W, F 2:30-4:25 –T, Th 4:00-5:15 First priority is for PH5452. No TA or instructor Handouts – Unix commands – How to run saturn from home

This Week Review of estimation and hypothesis testing Reading Le (review) –Chapter 4: Sections 4.1 – 4.3 –Chapter 5: Sections 5:1 and 5:4 –Chapter 7: Sections 7:1 – 7.3 Reading C &S –Chapter 2:A-E –Chapter 6: A,B,F

Steps in Creating and Running a SAS Program on Saturn 1.Create or edit SAS program (fn is name of program) > pico fn.sas (cntr x to exit) 2.Run the SAS program > sas fn.sas 3.List the files in directory - look for.log and.lst files > ls (or ls fn*) 4.View the.log file - look for errors and notes > less fn.log (type q to exit) 5.If errors go back to step 1 and repeat When no errors view.lst to view output > less fn.lst

Some Definitions Statistics: The art and science of collecting, analyzing, presenting, and interpreting data. Data: facts and figures that are collected Dataset: All the data collected for a study Elements: Units in which data is collected –People, companies, schools, households Variables: Characteristics measured on elements –People (height, weight) –Company (number of employees) –Schools (percentage of students who graduate in 5 years) –Households (number of computers owned)

Some Definitions Population: set of all elements of interest in a particular study –All persons in Minnesota 18-years or older –All Fortune 500 companies –All persons with hypertension –All persons who have colon cancer –All persons who could ever have colon cancer –All lab samples that could ever be analyzed Sample: a subset of the population A major contribution of statistics is that data from a sample can be used to make estimates and test hypothesis about the characteristics of a population. This process is referred to as statistical inference.

Informal Definition Statistics: In a scientific way gaining information about something you do not know

Start With Research Question What is the proportion of persons without health insurance in Minnesota? Do newer BP medications prevent heart disease compared to older medications? What is the relationship between grade point average and SAT scores Do persons who eat more F&V have lower risk of developing colon cancer. Does the program DARE reduce the risk of young persons trying drugs? What is the populations for each of these ?

Statistics Start With Question Start With Question Design Study And Collect Data Perform Analyses of Data to Assess Question. Perform Analyses of Data to Assess Question. Make Conclusions (Inference) Make Conclusions (Inference)

Statistical Inference Estimation (Chapter 4) Hypothesis Testing (Chapter 5) –Comparing population proportions (Chap 6) –Comparing population means (Chap 7)

Parameter: Numeric Characteristic of a Population ParameterParameter Description  Mean of population  Proportion with a certain trait  Correlation between 2 variables     Difference between 2 means     Difference between 2 proportions  Population standard deviation

Sampling Sample: a subset of target population (usually a simple random sample - each sample has equal probability of occurring) Different samples yield different estimates Trying to estimate the population parameter (the “true value”) –It’s usually not possible to measure the population value

Point Estimate Parameter Point Estimate  Sample mean  Sample proportion  Sample correlation     Difference between 2 sample means     Difference between 2 sample proportions  Sample standard deviation Sampling error: True value – estimate (unknown)

Statistical Inference Population with mean  = ? Population with mean  = ? A simple random sample of n elements is selected. from the population. The sample data provide a value for. the sample mean. The sample data provide a value for. the sample mean. The value of is used to make inferences about the value of . The value of is used to make inferences about the value of .

Interval Estimation In general, confidence intervals are of the form: SE = standard error of your estimate Estimate = mean, proportion, regression coefficient, odds ratio = for 95% CI based on normal distribution

Estimation “What is the average total cholesterol level for MN residents?” Random sample of cholesterol levels sample mean = sum of values / number of observations Estimates the population mean:

Estimation “What is the average total cholesterol level for MN residents?” sample standard deviation: estimates the population standard deviation:

Confidence Interval Example Suppose sample of 100 mean = 215 mg/dL, standard deviation = 20 95% CI = = ( *20/10, *20/10) approximately = (211, 219) = standard error of mean

Properties of Confidence Intervals As sample size increases, CI gets smaller –If you could sample the whole population; Can use different levels of confidence –90, 95, 99% common –More confidence means larger interval; so a 90% CI is smaller than a 99% CI Changes with population standard deviation –More variable population means larger interval

Caution with Confidence Intervals –Data should be from random sample –More complicated sampling requires different methods Example - multistage or stratified sampling –Outliers can cause problems –Non-normal data can change confidence level Skewed data a big problem –Bias not accounted for Non-responders Target and sampled population different

95% Confidence Intervals with SAS 1) Construct from output estimate +/- 1.96*SE 2) Provided automatically by some procedures PROC MEANS DATA = STUDENTS LCLM UCLM; VAR AGE;

Our Sample of 25 Replicates of n=10, 

True Sampling Distribution, n=10, 